Solve for $x$ and $y$ using elimination. ${-5x-3y = -44}$ ${4x+4y = 48}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $3$ ${-20x-12y = -176}$ $12x+12y = 144$ Add the top and bottom equations together. $-8x = -32$ $\dfrac{-8x}{{-8}} = \dfrac{-32}{{-8}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-5x-3y = -44}\thinspace$ to find $y$ ${-5}{(4)}{ - 3y = -44}$ $-20-3y = -44$ $-20{+20} - 3y = -44{+20}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 4}$ into $\thinspace {4x+4y = 48}\thinspace$ and get the same answer for $y$ : ${4}{(4)}{ + 4y = 48}$ ${y = 8}$